General
✓✗If \( \vec{A} = 2\hat{i} + 3\hat{j} - \hat{k} \) and \( \vec{B} = -\hat{i} + 3\hat{j} + 4\hat{k} \), the projection of \( \vec{A} \) on \( \vec{B} \) is
- \( \dfrac{3}{26} \)
- \( \dfrac{3}{\sqrt{14}} \)
- 3
- \( \dfrac{3}{\sqrt{26}} \)
General
✓✗A body moves on a circle of radius 5 m with speed 10 m/s. Its speed is increasing at 20 m s−2. The angle between its acceleration and velocity is
- 60°
- 90°
- 45°
- 30°
General
✓✗The result of \( \vec{A}\times\vec{0} \) will be equal to
- \( \vec{A} \)
- zero (scalar)
- zero vector
- unit vector
General
✓✗Two vectors of magnitudes 5 and 3 units have a scalar product of 7.5 units. The magnitude of their vector product is
- \( \dfrac{7.5}{\sqrt3} \)
- 15
- \( 7.5\sqrt{3} \)
- 7.5
General
✓✗A unit vector perpendicular to both \( \vec{A} = \hat{i} + \hat{j} \) and \( \vec{B} = \hat{j} + \hat{k} \) is
- \( \dfrac{1}{\sqrt{2}}(\hat{i} - \hat{k}) \)
- \( \hat{i} - \hat{j} + \hat{k} \)
- \( \dfrac{1}{\sqrt{3}}(\hat{i} - \hat{j} + \hat{k}) \)
- \( \dfrac{1}{\sqrt{3}}(\hat{i} + \hat{j} + \hat{k}) \)
General
✓✗The resultant of two vectors \( \vec{P} \) and \( \vec{Q} \) is perpendicular to \( \vec{P} \) and its magnitude is half that of \( \vec{Q} \). The angle between \( \vec{P} \) and \( \vec{Q} \) is
- 90°
- 150°
- 135°
- 120°
General
✓✗If the speed of a particle in uniform circular motion is doubled and the radius is halved, the centripetal acceleration becomes
- 4 times
- 2 times
- 8 times
- unchanged
General
✓✗For a projectile (air resistance neglected), the horizontal component of velocity
- decreases
- remains constant
- increases
- becomes zero at the top
General
✓✗A ball is thrown at 30° above the horizontal with 20 m/s from the top of a 20 m high building. It lands at a horizontal distance of about (take g = 10 m s−2)
- 35 m
- 56 m
- 40 m
- 17 m
General
✓✗A particle moving in the x-y plane has \( x = 2\cos 3t \) and \( y = 2\sin 3t \). The magnitude of its acceleration is
- 12 units
- 2 units
- 6 units
- 18 units
General
✓✗A man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the speeds of both (vm = speed of man, vB = speed of bag) on reaching the bottom are related as
- vB and vm cannot be related
- vB > vm
- vB < vm
- vB = vm
General
✓✗The vector product of two parallel vectors is
- equal to the product of magnitudes
- maximum
- a unit vector
- a null vector
General
✓✗The angular displacement of a particle in uniform circular motion of radius 2 m in which it covers an arc length of 3 m is
- 6 rad
- 3 rad
- 1.5 rad
- 0.67 rad
General
✓✗A ball rolls off a stair with horizontal speed 1.5 m/s. Each step is 20 cm high and 20 cm wide. Which step does the ball hit first? (take g = 10 m s−2)
- the 2nd step
- the 5th step
- the 1st step
- the 3rd step
General
✓✗The position vector of a point (3 m, 4 m) in the x-y plane, with respect to the origin, has a magnitude of
- 5 m
- 12 m
- 1 m
- 7 m